A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Let BC is Pedestal and AB is 1.6 m high statue.
In ΔBCD,
BC/CD = tan 45° ⇒ BC/CD = 1 ⇒ BC = CD
In ΔACD,
AB+BC/CD = tan 60° ⇒ AB+BC/BC = √3
⇒ 1.6 + BC/BC = √3
⇒ BC + 1.6 = BC√3
⇒ 1.6 = BC (√3 – 1)
⇒ BC = 1.6/(√3-1) × (√3+1)/(√3+1) = 1.6(√3+1)/2
= 0.8(√3+1)
Hence, the height of the pedestal is 0.8(√3+1)m.